Question

The intersection of asymptotes of root loci of a system with open loop transfer function G(s)H(s) = K/s(s+1)(s+3) is

(a) 1.44

(b) 1.33

(c) -1.44

(d) -1.33

The question was posed to me during a job interview.

This intriguing question comes from Construction of Root Loci in division The Root Locus Technique of Control Systems

Answer 1

The correct answer is (d) -1.33

The explanation: The intersection of asymptotes of root loci of a system is same as the centroid which is centroid =Σreal part of open loop pole-Σreal part of open loop zeroes/P-Z.

Centroid = -4/3=-1.33.